Numpy 基礎

NumPy 是 Python語言的一個擴充程式庫。

支援高階大規模的多維陣列與矩陣運算，
此外也針對陣列運算提供大量的數學函式函式庫。

向量 vector

Vector is ordered arrays of numbers.
In notation, vectors are denoted with lower case bold letters such as x.
The elements of a vector are all the same type (dtype).
The number of elements in the array
is often referred to as the dimension
though mathematicians may prefer rank.

Vector Creation

Slicing and Indexing

Indexing

a = np.arange(10) # [0 1 2 3 4 5 6 7 8 9]
print(a[2])       # 2
print(a[-1])      # a[-1] := a[len(a) - 1] = 9

向量運算

 使用 for 迴圈進行向量運算

使用 numpy

向量加減	x + y
Negate elements of x.	–x
純量乘法 (Scalar Multiplication) | Scalar Vector operations	w * x
內積 (Dot Product)	np.dot(x, y)
Sum of all elements of x.	a = np.sum(x)
Mean of all elements of x.	a = np.mean(x)
Create a vector y which ith element of y is ith element of x to the power of a.	y = x ** a

矩陣 Matrix

Matrix, are 2-D (two dimensional) arrays.
Matrices are denoted with capitol, bold letter such as X.
m is often the number of rows and n the number of columns.

$$ \textbf{X} = \left[
\begin{array}
x_{00} & x_{01} & … & x_{0(n-1)} \\
x_{10} & x_{11} & … & x_{1(n-1)} \\
… & … & … & … \\
x_{(m-1)0} & x_{(m-1)1} & … & x_{(m-1)(n-1)}
\end{array}
\right]_{ \ m \times n} $$

陣列 Array

Array Creation

np.zeros(d_0, d_1, …)

np.shape(array)

Return a tuple of ints, 
the elements of the tuple
give the lengths of the corresponding array dimensions.

x = np.zeros(4, 3)
"""
x = [ [0. 0. 0.]
      [0. 0. 0.]
      [0. 0. 0.]
      [0. 0. 0.]]
"""

print(np.shape(x)) # (4, 3)

Last Updated on 2023/08/16 by A1go